Fracture toughness of hierarchical lattice materials

Akseli Leraillez, Luc St-Pierre*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Natural materials, such as wood and bone, have a high fracture toughness and this is often attributed to their hierarchical microstructures. While previous studies have shown that hierarchy can increase the buckling strength of lattice materials, a detailed analysis of its impact on fracture toughness is missing. Here, we used analytical modeling and finite element simulations to predict the mode I and mode II fracture toughness of three hierarchical topologies: hexagonal, triangular, and Kagome lattices. Hierarchy significantly improved the fracture toughness of the bending-dominated hexagonal lattice. Notably, the hierarchical hexagonal lattice has a fracture toughness KIC that scales linearly with relative density ρ̄, whereas its non-hierarchical counterpart has KIC∝ρ̄2. In contrast, hierarchy did not improve the toughness of stretching-dominated triangular and Kagome lattices. Hierarchy did, however, modify the behavior of a Kagome lattice: its hierarchical design has a toughness that scales linearly with relative density, whereas KIC∝ρ̄ for its non-hierarchical counterpart. This work presents scaling laws for the fracture toughness of hierarchical lattices, enabling the design of tough architectures at very low densities.

Original languageEnglish
Article number113374
Number of pages14
JournalInternational Journal of Solids and Structures
Volume316
DOIs
Publication statusPublished - 15 Jun 2025
MoE publication typeA1 Journal article-refereed

Keywords

  • Finite Element simulation
  • Fracture toughness
  • Hierarchy
  • Honeycomb
  • Lattice material

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